PRICING SUPPLEMENT NO. 34                                         Rule 424(b)(3)
DATED: August 23, 2004                                       File No. 333-109793
(To Prospectus dated November 17, 2003,
and Prospectus Supplement dated November 17, 2003)

                                 $10,668,950,162
                         THE BEAR STEARNS COMPANIES INC.
                           Medium-Term Notes, Series B

Principal Amount: $8,500,000    Floating Rate Notes [x]   Book Entry Notes [x]

Original Issue Date: 9/15/2004  Fixed Rate Notes [ ]     Certificated Notes [ ]

Maturity Date:  9/15/2012       CUSIP#: 073928G80

                                Euroclear and Clearstream Common Code: 020083140

Option to Extend Maturity:      No   [x]
                                Yes  [ ]  Final Maturity Date:

Minimum Denominations: $100,000, increased in multiples of $10,000

                                              Optional            Optional
                         Redemption           Repayment           Repayment
   Redeemable On          Price(s)             Date(s)            Price(s)
   -------------         ----------           ---------           ---------
         *                    *                  N/A                 N/A

Applicable Only to Fixed Rate Notes:
-----------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
--------------------------------------

Interest Rate Basis:                    Maximum Interest Rate:  N/A

[ ]  Commercial Paper Rate              Minimum Interest Rate:  0.00%

[ ]  Federal Funds Effective Rate

[ ]  Federal Funds Open Rate            Interest Reset Date(s):  **

[ ]  Treasury Rate                      Interest Reset Period:  Quarterly

[ ]  LIBOR Reuters                      Interest Payment Date(s):  ***

[x]  LIBOR Telerate +

[ ]  Prime Rate

[ ]  CMT Rate



Interest Rate: Cliquet Inverse           Interest Payment Period:  Quarterly
               Floating Rate+
               See Annex A

Index Maturity:  Six Months              Interest Determination Date(s): 5th
                                         London Banking Day prior to but not
                                         including the last day of the
                                         immediately preceding Interest Payment
                                         Period, and for purposes of this
                                         provision only, without giving effect
                                         to the Business Day Convention (as
                                         defined in Annex A below)

Spread (plus or minus):  N/A             Day Count Basis:  360-day year of
                                                           twelve 30-day months

*     Commencing December 15, 2004 and on each Interest Payment Date thereafter
      until Maturity, the Notes may be called in whole at par at the option of
      the Company on five Business Days' notice. For purposes of this provision
      only, "Business Day" means any day that is not a Saturday or Sunday, and
      that is neither a legal holiday nor a day on which banking institutions or
      trust companies in New York City are authorized or obligated by law to
      close.

**    Commencing December 15, 2004 and on the 15th of each March, June,
      September and December prior to Maturity.

***   Commencing December 15, 2004 and on the 15th of each March, June,
      September and December thereafter, including the maturity date.

                  CERTAIN US FEDERAL INCOME TAX CONSIDERATIONS

      The following discussion summarizes certain US federal income tax
consequences of the purchase, beneficial ownership and disposition of the
Cliquet Inverse Floating Rate Notes (the "Notes"). This discussion supplements
the section captioned "Certain US Federal Income Tax Considerations" in the
Prospectus Supplement dated November 17, 2003. Except as provided below under
"Federal Income Tax Treatment of Non-US Holders," this summary deals only with a
beneficial owner of a Note that is:

o     an individual who is a citizen or resident of the United States for US
      federal income tax purposes;

o     a corporation (or other entity that is treated as a corporation for US
      federal tax purposes) that is created or organized in or under the laws of
      the United States or any State thereof (including the District of
      Columbia);

o     an estate whose income is subject to US federal income taxation regardless
      of its source; or

o     a trust if a court within the United States is able to exercise primary
      supervision over its administration, and one or more United States persons
      have the authority to control all of its substantial decisions (each, a
      "US Holder").

      If a partnership (or other entity that is treated as a partnership for US
federal tax purposes) is a beneficial owner of Notes, the treatment of a partner
in the partnership will generally depend upon the status of the partner and upon
the activities of the partnership. A beneficial owner of Notes that is a
partnership, and partners in such a partnership, should consult their tax
advisors about the US federal income tax consequences of holding and disposing
of the Notes.

      An individual may, subject to certain exceptions, be deemed to be a
resident of the United States for US federal income tax purposes by reason of
being present in the United States for at least 31 days in the calendar year and
for an aggregate of at least 83 days during a three-year period ending in the
current calendar year (counting for


                                      -2-


such purposes all of the days present in the current year, one-third of the days
present in the immediately preceding year, and one-sixth of the days present in
the second preceding year).

      This discussion is based on interpretations of the Internal Revenue Code
of 1986, as amended (the "Code"), regulations issued there under, and rulings
and decisions currently in effect (or in some cases proposed), all of which are
subject to change. Any such change may be applied retroactively and may
adversely affect the federal income tax consequences described in this Pricing
Supplement. This summary addresses only US Holders that purchase Notes at
initial issuance and beneficially own such Notes as capital assets and not as
part of a "straddle," "hedge," "synthetic security" or a "conversion
transaction" for federal income tax purposes, or as part of some other
integrated investment. This summary does not discuss all of the tax consequences
that may be relevant to particular investors or to investors subject to special
treatment under the federal income tax laws (such as S corporations, banks,
thrifts, other financial institutions, insurance companies, mutual funds, small
business investment companies, tax-exempt organizations, retirement plans, real
estate investment trusts, regulated investment companies, securities dealers or
brokers, traders in securities electing mark to market treatment, investors
whose functional currency is not the US dollar, persons subject to the
alternative minimum tax, and former citizens or residents of the United States),
and this summary does not discuss the tax consequences under the laws of any
foreign, state or local taxing jurisdictions. Accordingly, prospective investors
are urged to consult their tax advisors with respect to the federal, state and
local tax consequences of investing in the Notes, as well as any consequences
arising under the laws of any other taxing jurisdiction to which they may be
subject.

      PROSPECTIVE PURCHASERS OF NOTES SHOULD CONSULT THEIR TAX ADVISORS AS TO
THE FEDERAL, STATE, LOCAL, AND OTHER TAX CONSEQUENCES TO THEM OF THE PURCHASE,
OWNERSHIP AND DISPOSITION OF NOTES.

Federal Income Tax Treatment of US Holders.

      General

      There are no regulations, rulings or other authorities addressing the
federal income tax treatment of debt instruments with terms that are
substantially similar to the Notes, and therefore the federal income tax
treatment of the Notes is subject to some uncertainty.

      Under certain Treasury regulations addressing the timing and character of
income, gain, loss and deduction in respect of debt instruments (the "the OID
regulations"), for purposes of determining the yield and maturity of a debt
instrument, an issuer is generally deemed to exercise a call option in a manner
that minimizes the yield on the debt instrument. The OID regulations do not
indicate how this rule is applied to debt instruments, such as the Notes, that
provide for an inverse floating rate of interest and are callable at par. We
intend to take the position that for purposes of applying this rule, the yield
on the Notes should be calculated assuming each Quarterly Coupon is computed
based on the 6 Month USD LIBOR rate in effect on the date the Notes are issued.
Based on this assumption, our yield would be minimized by exercising our call on
September 15, 2005 and therefore, for purposes of the OID regulations, the Notes
would be treated as bearing interest at the initial Interest Rate and having a
maturity of twelve months. This assumption has been made solely for federal
income tax purposes in order to comply with the OID regulations. This assumption
does not necessarily reflect our expectations regarding the actual yield on the
Notes, nor is it an indication of our intention regarding whether or not to call
the Notes at any time.

      Under this position, the Quarterly Coupon on a Note for the initial
Interest Payment Period will be taxable to a US Holder as ordinary interest
income at the time it accrues or is received in accordance with the US Holder's
normal method of accounting for tax purposes. If we do not call the Notes on
September 15, 2005, solely for purposes of the OID regulations, the Notes would
be deemed to be retired and reissued at the end of the initial Interest Payment
Period and at the end of each subsequent Interest Payment Period. In this event,
a US Holder would not recognize gain or loss in respect of such deemed
retirement and reissuance and the Quarterly Coupon


                                      -3-


for the subsequent Interest Payment Period would be taxable to the US Holder as
ordinary interest income at the time it accrues or is received in accordance
with the US Holder's normal method of accounting for tax purposes calculated
based upon the 6 Month USD LIBOR rate in effect at that time.

      Sale, Exchange, Redemption, Repayment or Other Disposition of the Notes

      Under the approach described above, upon the disposition of a Note by
sale, exchange, redemption (if we exercise our call right or otherwise),
repayment or other disposition, a US Holder will generally recognize taxable
gain or loss equal to the difference, if any, between (i) the amount realized on
the disposition (other than amounts attributable to accrued but unpaid interest,
which would be treated as such) and (ii) the US Holder's adjusted tax basis in
the Note. A US Holder's adjusted tax basis in a Note generally will equal the
cost of the Note (net of accrued interest) to the US Holder. Capital gains of
individual taxpayers from the sale, exchange, redemption, repayment or other
disposition of a Note held for more than one year may be eligible for reduced
rates of taxation. The deductibility of a capital loss realized on the sale,
exchange, redemption, repayment or other disposition of a Note is subject to
limitations.

      Alternative Treatment

      As mentioned above, there are no regulations, rulings or other authorities
addressing the federal income tax treatment of debt instruments with terms that
are substantially similar to the Notes, and therefore the federal income tax
treatment of the Notes is subject to some uncertainty. Accordingly, other
treatments of the Notes are possible. For example, in the event that we are not
deemed to exercise our right to call the Notes for purposes of the OID
regulations on September 15, 2005, it is possible that the Notes could be
treated as "contingent payment debt instruments" for federal income tax
purposes. If the Notes were treated as contingent payment debt instruments for
federal income tax purposes, the timing and character of income with respect to
the Notes would be significantly affected. For example, a US Holder would be
required to include in income in each year an amount equal to the "comparable
yield" of the Notes, which is generally equal to the yield at which we would
issue a noncontingent debt instrument with terms and conditions similar to the
Notes. In addition, a "projected payment schedule" would be computed as of the
Original Issue Date that would produce the comparable yield. Furthermore, any
gain realized on the maturity date or upon an earlier call, sale, exchange or
other disposition of the Notes would generally be treated as ordinary income,
and any loss realized on the maturity date or upon an earlier call, sale,
exchange or other disposition of the Notes would be treated as ordinary loss to
the extent of interest included as income in the current or previous taxable
years by the US Holder in respect of the Notes, and capital loss thereafter. The
federal income tax treatment of contingent payment debt instruments is
summarized in the Prospectus Supplement dated November 17, 2003 under the
caption "Certain US Federal Income Tax Considerations - Contingent Payment Debt
Instruments."

Disclosure Requirements for Certain US Holders Recognizing Significant Losses.

      A US Holder that is an individual or a partnership with one or more
noncorporate partners that claims a loss of $2 million or more in a taxable year
or $4 million or more in any combination of taxable years in respect of a Note
may be subject to certain disclosure requirements for "reportable transactions."
Prospective investors should consult their own tax advisors concerning any
possible disclosure obligation with respect to the Notes.

Federal Income Tax Treatment of Non-US Holders.

      As used in this discussion, the term "Non-US Holder" means a beneficial
owner of a Note that is, for US federal income tax purposes:

      o     a nonresident alien individual,

      o     a foreign corporation,


                                      -4-


      o     a foreign partnership,

      o     an estate whose income is not subject to US federal income tax on a
            net income basis, or

      o     a trust if no court within the United States is able to exercise
            primary jurisdiction over its administration or if no United States
            persons have the authority to control all of its substantial
            decisions.

      Payments on the Notes to Non-US Holders will not be subject to US federal
income or withholding tax if the following conditions are satisfied:

      o     the Non-US Holder does not actually or constructively own 10% or
            more of the total combined voting power of all classes of our stock
            entitled to vote,

      o     the Non-US Holder is not a controlled foreign corporation for US
            federal income tax purposes that is related to us through actual or
            constructive ownership,

      o     the Non-US Holder is not a bank receiving interest on a loan made in
            the ordinary course of its trade or business,

      o     interest payable on the Notes is not determined by reference to any
            receipts, sales or other cash flow, income or profits, change in the
            value of any property of, or any dividend or similar payment made by
            us or a person related to us, within the meaning of Code section
            871(h)(4)(A), and

      o     the payments are not effectively connected with a trade or business
            conducted by the Non-US Holder in the United Stated and either (a)
            the Non-US Holder provides a correct, complete and executed IRS Form
            W-8BEN or Form W-8IMY (or successor form) with all of the
            attachments required by the IRS, or (b) the Non-US Holder holds its
            Note through a qualified intermediary (generally a foreign financial
            institution or clearing organization or a non-US branch or office of
            a US financial institution or clearing organization that is a party
            to a withholding agreement with the IRS) which has provided to us an
            IRS Form W-8IMY stating that it is a qualified intermediary and has
            received documentation upon which it can rely to treat the payment
            as made to a foreign person.

      If any of these conditions is not satisfied, interest (including OID) on
the Notes will be subject to a 30% withholding tax when paid, unless an income
tax treaty reduces or eliminates the tax or the interest is effectively
connected with the conduct of a US trade or business and the Non-US Holder
provides a correct, complete and executed IRS Form W-8ECI.

      In general, gain realized on the sale, exchange or retirement of the Notes
by a Non-US Holder will not be subject to US federal income tax, unless:

      o     the gain with respect to the Notes is effectively connected with a
            trade or business conducted by the Non-US Holder in the United
            States, or

      o     the Non-US Holder is a nonresident alien individual who holds the
            Notes as a capital asset and is present in the United States for
            more than 182 days in the taxable year of the sale and certain other
            conditions are satisfied.

      A Note held by an individual who at death is a Non-US Holder will not be
includible in the individual's gross estate for US federal estate tax purposes
if payments on the Notes to the Non-US Holder would not have been subject to US
federal income or withholding tax at the time of death under the tests described
above.


                                      -5-


Information Reporting and Backup Withholding.

      Information reporting will apply to certain payments on a Note (including
interest and OID) and proceeds of the sale of a Note held by a US Holder that is
not an exempt recipient (such as a corporation). Backup withholding may apply to
payments made to a US Holder if (a) the US Holder has failed to provide its
correct taxpayer identification number on IRS Form W-9, (b) we have been
notified by the IRS of an underreporting by the US Holder (underreporting
generally refers to a determination by the IRS that a payee has failed to
include in income on its tax return any reportable dividend and interest
payments required to be shown on a tax return for a taxable year), or (c) we
have been notified by the IRS that the tax identification number provided to the
IRS on an information return does not match IRS records or that the number was
not on the information return.

Backup withholding will not be required with respect to Non-US Holders, so long
as we have received from the Non-US Holder a correct and complete IRS Form
W-8BEN or Form W-8IMY with all of the attachments required by the IRS, signed
under penalty of perjury, identifying the Non-US Holder and stating that the
Non-US Holder is not a United States person. In addition, IRS Form W-8BEN will
be required from the beneficial owners of interests in a Non-US Holder that is
treated as a partnership for U.S. federal income tax purposes. Interest paid to
a Non-US Holder will be reported on IRS Form 1042-S which is filed with the IRS
and sent to Non-US Holders.

Information reporting and backup withholding may apply to the proceeds of a sale
of a Note by a Non-US Holder made within the United States or conducted through
certain US related financial intermediaries, unless the payor receives the
statement described above.

Backup withholding is not an additional tax and may be refunded (or credited
against your US federal income tax liability, if any), provided, that certain
required information is furnished. The information reporting requirements may
apply regardless of whether withholding is required. For Non-US Holders, copies
of the information returns reporting such interest and withholding also may be
made available to the tax authorities in the country in which a Non-US Holder is
a resident under the provisions of an applicable income tax treaty or agreement.

THE PRECEDING DISCUSSION IS ONLY A SUMMARY OF CERTAIN OF THE TAX IMPLICATIONS OF
AN INVESTMENT IN NOTES. PROSPECTIVE PURCHASERS ARE URGED TO CONSULT WITH THEIR
OWN TAX ADVISORS PRIOR TO INVESTING TO DETERMINE THE TAX IMPLICATIONS OF SUCH
INVESTMENT IN LIGHT OF EACH SUCH INVESTOR'S PARTICULAR CIRCUMSTANCES.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.


                                      -6-


                                     Annex A

                          Cliquet Inverse Floating Rate

+ The Interest Rate for each Interest Payment Period shall be determined by the
Calculation Agent in accordance with the following:




------------------------------------------------------------------------------------------------------------
                  Interest Payment Period                                   Quarterly Coupon
------------------------------------------------------------------------------------------------------------
                                                          
For the Interest Payment Period from and including                        14.00% (initial Interest Rate)
September 15, 2004 to but excluding December 15, 2004
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including                        14.00%
December 15, 2004 to but excluding March 15, 2005
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including March                  14.00%
15, 2005 to but excluding June 15, 2005
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including June                   14.00%
15, 2005 to but excluding September 15, 2005
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 1.00% - 6 Month
September 15, 2005 to but excluding December 15, 2005        USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 1.00% - 6 Month
December 15, 2005 to but excluding March 15, 2006            USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including March     Previous Quarterly Coupon + 1.00% - 6 Month
15, 2006 to but excluding June 15, 2006                      USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including June      Previous Quarterly Coupon + 1.00% - 6 Month
15, 2006 to but excluding September 15, 2006                 USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 2.00% - 6 Month
September 15, 2006 to but excluding December 15, 2006        USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 2.00% - 6 Month
December 15, 2006 to but excluding March 15, 2007            USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including March     Previous Quarterly Coupon + 2.00% - 6 Month
15, 2007 to but excluding June 15, 2007                      USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including June      Previous Quarterly Coupon + 2.00% - 6 Month
15, 2007 to but excluding September 15, 2007                 USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 3.00% - 6 Month
September 15, 2007 to but excluding December 15, 2007        USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 3.00% - 6 Month
December 15, 2007 to but excluding March 15, 2008            USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including March     Previous Quarterly Coupon + 3.00% - 6 Month
15, 2008 to but excluding June 15, 2008                      USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including June      Previous Quarterly Coupon + 3.00% - 6 Month
15, 2008 to but excluding September 15, 2008                 USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 4.00% - 6 Month
September 15, 2008 to but excluding December 15, 2008        USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 4.00% - 6 Month
December 15, 2008 to but excluding March 15, 2009            USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including March     Previous Quarterly Coupon + 4.00% - 6 Month
15, 2009 to but excluding June 15, 2009                      USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including June      Previous Quarterly Coupon + 4.00% - 6 Month
15, 2009 to but excluding September 15, 2009                 USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 5.00% - 6 Month
September 15, 2009 to but excluding December 15, 2009        USD LIBOR
------------------------------------------------------------------------------------------------------------



                                      -7-



------------------------------------------------------------------------------------------------------------
                                                          
For the Interest Payment Period from and including           Previous Quarterly Coupon + 5.00% - 6 Month
December 15, 2009 to but excluding March 15, 2010            USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including March     Previous Quarterly Coupon + 5.00% - 6 Month
15, 2010 to but excluding June 15, 2010                      USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including June      Previous Quarterly Coupon + 5.00% - 6 Month
15, 2010 to but excluding September 15, 2010                 USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 6.00% - 6 Month
September 15, 2010 to but excluding December 15, 2010        USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 6.00% - 6 Month
December 15, 2010 to but excluding March 15, 2011            USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including March     Previous Quarterly Coupon + 6.00% - 6 Month
15, 2011 to but excluding June 15, 2011                      USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including June      Previous Quarterly Coupon + 6.00% - 6 Month
15, 2011 to but excluding September 15, 2011                 USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 7.00% - 6 Month
September 15, 2011 to but excluding December 15, 2011        USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including           Previous Quarterly Coupon + 7.00% - 6 Month
December 15, 2012 to but excluding March 15, 2012            USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including March     Previous Quarterly Coupon + 7.00% - 6 Month
15, 2012 to but excluding June 15, 2012                      USD LIBOR
------------------------------------------------------------------------------------------------------------
For the Interest Payment Period from and including June      Previous Quarterly Coupon + 7.00% - 6 Month
15, 2012 to but excluding September 15, 2012                 USD LIBOR
------------------------------------------------------------------------------------------------------------


      Previous Quarterly Coupon means the Interest Rate for the preceding
Interest Payment Period.

      With respect to any Interest Payment Period, 6 month USD LIBOR shall be
USD LIBOR set in arrears with a designated maturity of 6 months as published on
Telerate page 3750 on the fifth London Banking Day prior to but not including
the last day of the immediately preceding Interest Payment Period. For any
Interest Payment Period where 6 month USD LIBOR sets below 0.00%, 6 month USD
LIBOR shall be deemed to be 0.00% for that Interest Payment Period.

      If any Interest Reset Date would otherwise be a day that is not a Business
Day, such Interest Reset Date shall be postponed to the next succeeding day that
is a Business Day, except that if such Business Day is in the next succeeding
calendar month, such Interest Reset Date shall be the next preceding Business
Day (any such adjustment being referred to as the "Business Day Convention").
For purposes of determining an Interest Reset Date, "Business Day" means any day
that is not a Saturday or Sunday, and that is neither a legal holiday nor a day
on which banking institutions or trust companies in New York City are authorized
or obligated by law to close and which is also a London Banking Day. A "London
Banking Day" means any day on which dealings in deposits in U.S. dollars are
transacted in the London interbank market.


                                      -8-